Mercurial > octave-nkf
annotate scripts/signal/freqz.m @ 17281:bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Macro handles options ("on") or properties ("position") more elegantly
than @code{"text"}.
* doc/interpreter/macros.texi: Add new @qcode macro.
* doc/interpreter/tips.txi: Add documentation about @qcode macro.
* doc/interpreter/basics.txi, doc/interpreter/container.txi,
doc/interpreter/emacs.txi, doc/interpreter/errors.txi,
doc/interpreter/eval.txi, doc/interpreter/expr.txi,
doc/interpreter/external.txi, doc/interpreter/func.txi,
doc/interpreter/grammar.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/io.txi, doc/interpreter/matrix.txi,
doc/interpreter/numbers.txi, doc/interpreter/oop.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/quad.txi, doc/interpreter/sparse.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc,
libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc,
libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc,
libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc,
libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc,
libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc,
libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc,
libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m,
scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m,
scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m,
scripts/general/dblquad.m, scripts/general/display.m,
scripts/general/genvarname.m, scripts/general/idivide.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m,
scripts/general/profexplore.m, scripts/general/profile.m,
scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m,
scripts/general/subsindex.m, scripts/general/triplequad.m,
scripts/geometry/griddata.m, scripts/geometry/griddata3.m,
scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m,
scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m,
scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m,
scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m,
scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m,
scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m,
scripts/java/javaclasspath.m, scripts/java/usejava.m,
scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m,
scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m,
scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m,
scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m,
scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m,
scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m,
scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m,
scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m,
scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m,
scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m,
scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m,
scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m,
scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m,
scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m,
scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m,
scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m,
scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m,
scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m,
scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m,
scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m,
scripts/plot/plot.m, scripts/plot/print.m,
scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m,
scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m,
scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m,
scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m,
scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m,
scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m,
scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m,
scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m,
scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m,
scripts/polynomial/conv.m, scripts/polynomial/polyout.m,
scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m,
scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m,
scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m,
scripts/signal/periodogram.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m,
scripts/specfun/legendre.m, scripts/special-matrix/gallery.m,
scripts/statistics/base/mean.m, scripts/statistics/base/moment.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m,
scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m,
scripts/strings/index.m, scripts/strings/isstrprop.m,
scripts/strings/mat2str.m, scripts/strings/regexptranslate.m,
scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjust.m, scripts/strings/strmatch.m,
scripts/strings/validatestring.m, scripts/testfun/demo.m,
scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m,
scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m,
scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m,
scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m,
scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
| author | Rik <rik@octave.org> |
|---|---|
| date | Mon, 19 Aug 2013 20:46:38 -0700 |
| parents | b10a23fe80bb |
| children | b81b9d079515 |
| rev | line source |
|---|---|
|
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1 ## Copyright (C) 1994-2012 John W. Eaton |
| 2313 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 2313 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 2303 | 18 |
| 3367 | 19 ## -*- texinfo -*- |
|
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20 ## @deftypefn {Function File} {[@var{h}, @var{w}] =} freqz (@var{b}, @var{a}, @var{n}, "whole") |
|
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21 ## @deftypefnx {Function File} {@var{h} =} freqz (@var{b}, @var{a}, @var{w}) |
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22 ## @deftypefnx {Function File} {[@dots{}] =} freqz (@dots{}, @var{Fs}) |
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23 ## @deftypefnx {Function File} {} freqz (@dots{}) |
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24 ## |
| 3367 | 25 ## Return the complex frequency response @var{h} of the rational IIR filter |
| 26 ## whose numerator and denominator coefficients are @var{b} and @var{a}, | |
| 27 ## respectively. The response is evaluated at @var{n} angular frequencies | |
| 28 ## between 0 and | |
|
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29 ## @ifnottex |
| 3367 | 30 ## 2*pi. |
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31 ## @end ifnottex |
| 3367 | 32 ## @tex |
| 33 ## $2\pi$. | |
| 34 ## @end tex | |
| 3426 | 35 ## |
| 3367 | 36 ## @noindent |
| 37 ## The output value @var{w} is a vector of the frequencies. | |
| 3426 | 38 ## |
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39 ## If @var{a} is omitted, the denominator is assumed to be 1 (this |
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40 ## corresponds to a simple FIR filter). |
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41 ## |
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42 ## If @var{n} is omitted, a value of 512 is assumed. |
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43 ## |
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44 ## For fastest computation, @var{n} should factor into a small number of |
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45 ## small primes. |
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46 ## |
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47 ## If the fourth argument, @qcode{"whole"}, is omitted the response is |
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48 ## evaluated at frequencies between 0 and |
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49 ## @ifnottex |
| 3367 | 50 ## pi. |
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51 ## @end ifnottex |
| 3367 | 52 ## @tex |
| 53 ## $\pi$. | |
| 54 ## @end tex | |
| 3426 | 55 ## |
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56 ## @code{freqz (@var{b}, @var{a}, @var{w})} |
| 3426 | 57 ## |
| 3893 | 58 ## Evaluate the response at the specific frequencies in the vector @var{w}. |
| 59 ## The values for @var{w} are measured in radians. | |
| 60 ## | |
|
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61 ## @code{[@dots{}] = freqz (@dots{}, @var{Fs})} |
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62 ## |
| 3893 | 63 ## Return frequencies in Hz instead of radians assuming a sampling rate |
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64 ## @var{Fs}. If you are evaluating the response at specific frequencies |
| 3893 | 65 ## @var{w}, those frequencies should be requested in Hz rather than radians. |
| 66 ## | |
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parents:
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67 ## @code{freqz (@dots{})} |
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68 ## |
| 3907 | 69 ## Plot the pass band, stop band and phase response of @var{h} rather |
| 70 ## than returning them. | |
| 3367 | 71 ## @end deftypefn |
| 904 | 72 |
| 3367 | 73 ## Author: jwe ??? |
| 2314 | 74 |
| 5377 | 75 function [h_r, f_r] = freqz (b, a, n, region, Fs) |
| 566 | 76 |
| 3893 | 77 if (nargin < 1 || nargin > 5) |
| 6046 | 78 print_usage (); |
| 3893 | 79 elseif (nargin == 1) |
| 2303 | 80 ## Response of an FIR filter. |
| 3893 | 81 a = n = region = Fs = []; |
| 566 | 82 elseif (nargin == 2) |
| 2303 | 83 ## Response of an IIR filter |
| 3893 | 84 n = region = Fs = []; |
| 566 | 85 elseif (nargin == 3) |
| 3893 | 86 region = Fs = []; |
| 566 | 87 elseif (nargin == 4) |
| 3893 | 88 Fs = []; |
| 5443 | 89 if (! ischar (region) && ! isempty (region)) |
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90 Fs = region; |
| 3893 | 91 region = []; |
| 92 endif | |
| 93 endif | |
| 94 | |
| 5377 | 95 if (isempty (b)) |
| 96 b = 1; | |
| 97 endif | |
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98 if (isempty (a)) |
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99 a = 1; |
| 3893 | 100 endif |
| 101 if (isempty (n)) | |
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102 n = 512; |
| 3893 | 103 endif |
| 104 if (isempty (region)) | |
| 105 if (isreal (b) && isreal (a)) | |
| 106 region = "half"; | |
| 107 else | |
| 108 region = "whole"; | |
| 109 endif | |
| 110 endif | |
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111 if (isempty (Fs)) |
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112 if (nargout == 0) |
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113 Fs = 2; |
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114 else |
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115 Fs = 2*pi; |
| 3893 | 116 endif |
| 566 | 117 endif |
| 118 | |
| 5583 | 119 a = a(:); |
| 120 b = b(:); | |
| 566 | 121 |
| 8506 | 122 if (! isscalar (n)) |
| 123 ## Explicit frequency vector given | |
| 5377 | 124 w = f = n; |
| 8506 | 125 if (nargin == 4) |
| 126 ## Sampling rate Fs was specified | |
| 5377 | 127 w = 2*pi*f/Fs; |
| 566 | 128 endif |
| 5986 | 129 k = max (length (b), length (a)); |
| 130 hb = polyval (postpad (b, k), exp (j*w)); | |
| 131 ha = polyval (postpad (a, k), exp (j*w)); | |
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132 else |
| 5583 | 133 ## polyval(fliplr(P),exp(jw)) is O(p n) and fft(x) is O(n log(n)), |
| 6653 | 134 ## where p is the order of the polynomial P. For small p it |
| 5377 | 135 ## would be faster to use polyval but in practice the overhead for |
| 136 ## polyval is much higher and the little bit of time saved isn't | |
| 137 ## worth the extra code. | |
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138 k = max (length (b), length (a)); |
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139 if (k > n/2 && nargout == 0) |
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140 ## Ensure a causal phase response. |
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141 n = n * 2 .^ ceil (log2 (2*k/n)); |
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142 endif |
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143 |
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144 if (strcmp (region, "whole")) |
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145 N = n; |
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146 else |
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147 N = 2*n; |
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148 endif |
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149 |
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150 f = Fs * (0:n-1).' / N; |
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151 |
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152 pad_sz = N*ceil (k/N); |
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153 b = postpad (b, pad_sz); |
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154 a = postpad (a, pad_sz); |
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155 |
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156 hb = zeros (n, 1); |
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157 ha = zeros (n, 1); |
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158 |
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159 for i = 1:N:pad_sz |
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160 hb = hb + fft (postpad (b(i:i+N-1), N))(1:n); |
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161 ha = ha + fft (postpad (a(i:i+N-1), N))(1:n); |
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162 endfor |
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163 |
| 566 | 164 endif |
| 165 | |
| 3893 | 166 h = hb ./ ha; |
| 167 | |
| 8506 | 168 if (nargout != 0) |
| 169 ## Return values and don't plot. | |
| 3907 | 170 h_r = h; |
| 5377 | 171 f_r = f; |
| 8506 | 172 else |
| 173 ## Plot and don't return values. | |
| 5377 | 174 freqz_plot (f, h); |
| 7151 | 175 endif |
| 3907 | 176 |
| 566 | 177 endfunction |
| 5377 | 178 |
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179 |
| 5377 | 180 %!test # correct values and fft-polyval consistency |
| 181 %! # butterworth filter, order 2, cutoff pi/2 radians | |
| 182 %! b = [0.292893218813452 0.585786437626905 0.292893218813452]; | |
| 183 %! a = [1 0 0.171572875253810]; | |
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184 %! [h,w] = freqz (b,a,32); |
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185 %! assert (h(1),1,10*eps); |
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186 %! assert (abs (h(17)).^2,0.5,10*eps); |
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187 %! assert (h,freqz (b,a,w),10*eps); # fft should be consistent with polyval |
| 5377 | 188 |
| 189 %!test # whole-half consistency | |
| 190 %! b = [1 1 1]/3; # 3-sample average | |
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191 %! [h,w] = freqz (b,1,32,"whole"); |
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192 %! assert (h(2:16),conj (h(32:-1:18)),20*eps); |
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193 %! [h2,w2] = freqz (b,1,16,"half"); |
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194 %! assert (h(1:16),h2,20*eps); |
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195 %! assert (w(1:16),w2,20*eps); |
| 5377 | 196 |
| 197 %!test # Sampling frequency properly interpreted | |
| 5986 | 198 %! b = [1 1 1]/3; a = [1 0.2]; |
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199 %! [h,f] = freqz (b,a,16,320); |
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200 %! assert (f,[0:15]'*10,10*eps); |
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201 %! [h2,f2] = freqz (b,a,[0:15]*10,320); |
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202 %! assert (f2,[0:15]*10,10*eps); |
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203 %! assert (h,h2.',20*eps); |
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204 %! [h3,f3] = freqz (b,a,32,"whole",320); |
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205 %! assert (f3,[0:31]'*10,10*eps); |